111 Communications Fall 2008 NCTU EE Tzu-Hsien Sang.
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111
Communications
Fall 2008
NCTU EE
Tzu-Hsien Sang
22
Outlines
• Linear Modulation
• Angle Modulation
• Interference
• Feedback Demodulators
• Analog Pulse Modulation
• Delta Modulation and PCM
• Multiplexing
2
3
Phase-Lock Loops (PLL) for FM Demodulation
• Tracks the instantaneous angle (phase and frequency) of the input signal.
(1) phase detector (comparator)
(2) loop filter
(3) loop amplifier
(4) VCO (voltage-controlled oscillator)
4
)).()(sin(2
)( :Example
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)).()(()( :Detector Phase
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)](sin[)( :ouput VCO The
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age.input volt the
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6
• Analysis of PLL: first, simplification, of course. Assume that the frequency matches, look at the phase difference.
(1) Non-linear Model:
7
).()())()(sin( ,)()( If
:ModelLinear )2(
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8
• Now we will present classical PLL analysis with classification on different loop filters.
<Case 1> Loop filter = 1
)).()(sin()(
))()(sin()()(
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)(
modelNonlinear (i)
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9
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11
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:Remarks
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12
13.
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2
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14
better. theis, larger the:Note
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15
• First-order PLL summary
1.Limited lock range
2.Nonzero steady state error
3.The complete system loop gain is
4.Kt also controls the bandwidth of PLL
5.A large Kt is impractical since (a) hardware implementation issues and (b) noise increases due to the wide bandwidth.
To overcome some of the drawbacks, move to higher-order PLL.
VdCt KkAAK v2
1
t
t
Ks
KsH
)(
16
<Case 2> Perfect 2nd-order PLL
Use the linear model to analyze.
)].()()[()(
./)()(filter loop The
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t
17
function.sfer order tran 2nd typicala of form in the is This
factor). (damping 2
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frequency) (natural where
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output. tracking theandinput ebetween th difference out the figure Then,
.)(
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)()(
function. transfer loop-close thefind First,
22
2
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18(rad). 2 iserror phase statesteady the:slipping-Cycle
.phenomenon slipping"-cycle" has PLL But the
unlimited! is rangelock The
:Remarks
error).frequency statesteady (no 0 as 0)(
.1for )1sin(1
)(
.22
)(
domain) (in .)(
domain) (in time ).()(
input frequency step of Analysis
2
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m
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19
20
• Applications of PLL
(1) Frequency multiplier: Generate the harmonics of the input and the VCO tracks one of the harmonics.
21
(2) Frequency divider: Generate the harmonics of the VCO output. One of the harmonics tracks the input.
22
(3) FM demodulator
Implementation of the phase detector:
Phase
detector Loop filter & amplifier
VCO
xr(t) ed(t)
eo(t)
eV(t) Demodulated
output
)()(
)( tmdt
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LPF xr(t)=ACcos[ct+(t)]
y(t) ed(t)
eo(t)=AVsin(ct+(t))
).()()]()(sin[ small, is )]()([When
)]()(sin[2
)(
)]()(sin[2
)]()(2sin[2
)()()(
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